For achieving long distance optical signal transmission, at moderate spectral efficiencies, dual polarization Binary Phase Shift Keying (DP-BPSK) and coherent reception are commonly used. As is known in the art, BPSK encodes a single bit value (“0” or “1”) onto an optical carrier by modulating the carrier phase between two constellation points, that are separated by 180°. Dual polarization BPSK achieves a spectral efficiency of 2-bits per symbol period (baud), by independently modulating bits onto orthogonal polarizations of the optical carrier. This is illustrated in FIG. 1, which shows the BPSK constellation mapped onto the Real (Re)-Imaginary (Im) plane of each of the X- and Y-polarizations.
As is known in the art, other modulation schemes enable increased numbers of bits to be encoded into a symbol. For example, Quadrature Phase Shift Keying (QPSK) enables two bits to be encoded on each polarization, and thus four bits per baud for dual polarization DP-QPSK, by using a symmetrical 4-point constellation as may be seen in FIG. 2. Other modulation schemes, such as Quadrature Amplitude Modulation (QAM) achieve even higher numbers of bits per symbol by modulating both the phase and amplitude of the carrier. However, as the number of encoded bits-per-symbol increases, the Euclidian distance between neighbouring constellation points decreases. For example, in the BPSK constellations shown in FIG. 1, each constellation point is separated from its neighbour by a Euclidean distance corresponding to 180°. On the other hand, in the QPSK constellations shown in FIG. 2, each constellation point is separated from its neighbour by a Euclidean distance corresponding to 90°. The reduced separation between adjacent constellation points results in a corresponding decrease in noise tolerance.
Because BPSK maximizes the Euclidian distance between adjacent points in the constellation, it is favoured for long distance transmission (for example under-sea fiber links) and other links having a low signal-to-noise ratio, in spite of the higher spectral efficiency achievable using other modulation schemes. The use of dual polarization BPSK (DP-BPSK) increases spectral efficiency, but is vulnerable to polarization-dependent impairments, such as Polarization Dependent Loss (PDL).
“Polarization QAM Modulation (POL-QAM) for Coherent Detection Schemes”, H. Bulow, OSA/OFC/NFOEC 2009, describes the use of a sphere packing constellation in the four optical dimensions (XI, XQ, YI, and YQ, representing I and Q axes of each of the X- and Y-polarizations). This constellation has 24 constellation points which encodes a little more than four bits per symbol.
“Power-Efficient Modulation Formats in Coherent Transmission Systems” Agrell et al, Journal Of Lightwave Technology, Vol. 27, No. 22, Nov. 15, 2009, describes a three bit per symbol constellation because of its performance at very high signal to noise ratios. In FIG. 6 they also show a point for a tetrahedron constellation that encodes two bits per symbol, that also works well at very high signal to noise ratios. However, modern coherent optical transmission systems typically operate at very low signal to noise ratios with forward error correction able to correct several percent errors. Cross polarization modulation also can be severe.
“Beyond 240 Gb/s per Wavelength Optical Transmission Using Coded Hybrid Subcarrier/Amplitude/Phase/Polarization Modulation”, Djordjevic et al, IEEE Photonics Technology Letters, Vol. 22, No. 5, Mar. 1, 2010, describes modulating codes onto three of the four optical dimensions, expressed as three stokes parameters. However, as this leaves one dimension unused it has reduced performance.
Techniques that enable improved spectral efficiency at low signal-to-noise ratios remain highly desirable.